A NOTE ON FINITE C-TIDY GROUPS

Let G be a group and x 2 G. The cyclicizer of x is dened to be the subset Cyc(x) = fy 2 G j hx; yi is cyclicg. G is said to be a tidy group if Cyc(x) is a subgroup for all x 2 G. We call G to be a C-tidy group if Cyc(x) is a cyclic subgroup for all x 2 G n K(G), where K(G) is the intersection of all the cyclicizers in G. In this note, we classify finite C-tidy groups with K(G) = f1g.